Finite Group Databasebeta

← #26183473

Subgroups — #26183473

Order 12032.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257408C211yesmaximal, characteristic
2#20252424C211yesmaximal, characteristic, complemented
3#20245746C211yesmaximal, characteristic, complemented
4#20241912C211yesmaximal, characteristic, complemented
5#20241905C211yesmaximal, characteristic, complemented
6#20241902C211yesmaximal, characteristic, complemented
7#20241894C211yesmaximal, characteristic, complemented
8#20241891C211yesmaximal, characteristic, complemented
9#20241881C211yesmaximal, characteristic, complemented
10#20241879C211yesmaximal, characteristic, complemented
11#20241878C211yesmaximal, characteristic, complemented
12#20241873C211yesmaximal, characteristic, complemented
13C2×#15688856C211yesmaximal, characteristic, complemented
14#327×D47C211yesmaximal, characteristic, complemented
15C47×#1504C211yesmaximal, characteristic, complemented
16#15689836C411yescharacteristic, complemented
17#15689831C411yescharacteristic, complemented
18#15689825C411yescharacteristic, complemented
19#15689822—21no—
20#15689817C411yescharacteristic, complemented
21#15689792C411yescharacteristic, complemented
22#15689768—21no—
23#15689764C411yescharacteristic, complemented
24#15689761C411yescharacteristic, complemented
25#15689760—21no—
26#15689757C411yescharacteristic, complemented
27#15689755—21no—
28#15689725—21no—
29#15689709—21no—
30#15689706—21no—
31#15689668C2211yescharacteristic
32#15689659C2211yescharacteristic
33#15689636C2211yescharacteristic
34C2×#13093998C2211yescharacteristic
35#121×D47C2211yescharacteristic
36#15689595—21no—
37C2×C4×C22⋊D47—21no—
38C2×C4×C22⋊D47C2211yescharacteristic
39#15689199—21no—
40#15689192—21no—
41#15689191—21no—
42(C22⋊D47)⋊C8—21no—
43#15689177C2211yescharacteristic, complemented
44#15689173C2211yescharacteristic, complemented
45#15689085C2211yescharacteristic, complemented
46C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
47C22⋊C8×D47C2211yescharacteristic, complemented
48#15688974—21no—
49#15688974C2211yescharacteristic, complemented
50C4×C22⋊Dic47—21no—
51C4×C22⋊Dic47C2211yescharacteristic, complemented
52#15688970—21no—
53#15688970C2211yescharacteristic, complemented
54#15688968C2211yescharacteristic, complemented
55#95×D47C2211yescharacteristic, complemented
56#15688860C2211yescharacteristic, complemented
57#15688860C2211yescharacteristic, complemented
58#15688858C2211yescharacteristic
59#15688858C2211yescharacteristic
60#15688858C2211yescharacteristic, complemented
61#15688858C2211yescharacteristic, complemented
62#15688857C2211yescharacteristic, complemented
63#15688857C2211yescharacteristic, complemented
64#15688856C2211yescharacteristic
65#15688856C2211yescharacteristic
66#15688856C2211yescharacteristic, complemented
67#15688856C2211yescharacteristic, complemented
68C47×#525C2211yescharacteristic
69C47×#407C2211yescharacteristic, complemented
70C2×#95×C47C2211yescharacteristic, complemented
71C47×#328C2211yescharacteristic, complemented
72C47×#328C2211yescharacteristic, complemented
73C47×#327C2211yescharacteristic, complemented
74C47×#327C2211yescharacteristic, complemented
75C2×#10625354C2×C411yescharacteristic, complemented
76C2×#10625352—21no—
77C22×D188C2×C411yescharacteristic, complemented
78C22×C22⋊D47—21no—
79C22×C22⋊D47D411yescharacteristic
80C2×D4×D47—21no—
81C2×D4×D47—21no—
82C2×D4×D47C2×C411yescharacteristic, complemented
83C22×C4×D47—21no—
84C22×C4×D47C2311yescharacteristic
85C2×#10625324—21no—
86C22×C47⋊C8—21no—
87C2×C8×D47—21no—
88#13094023C2×C411yescharacteristic, complemented
89#13094020—21no—
90#13094020C2×C411yescharacteristic, complemented
91#13094019—21no—
92#13094018—21no—
93#13094017—21no—
94#13094015C2×C411yescharacteristic, complemented
95#13094014—21no—
96#13094013C2×C411yescharacteristic, complemented
97#13094012—21no—
98#13094010—21no—
99#13094010—21no—
100#13094009—21no—
101#13094009—21no—
102#13094008—21no—
103#13094008—21no—
104#13094007—21no—
105#13094006—21no—
106#13094004—21no—
107#13094001—21no—
108#13094000C2×C411yescharacteristic, complemented
109#13093999—21no—
110#13093999C2×C411yescharacteristic, complemented
111#13093999C2×C411yescharacteristic, complemented
112#13093998—21no—
113#13093998—21no—
114#13093998—21no—
115#13093998C2×C411yescharacteristic, complemented
116#13093998C2×C411yescharacteristic, complemented
117#13093998C2311yescharacteristic
118#13093998C2311yescharacteristic
119#13093997—21no—
120#13093997—21no—
121#13093997—21no—
122#13093997—21no—
123#13093996—21no—
124#13093996—21no—
125#13093996—21no—
126#13093996—21no—
127#13093995—21no—
128#13093995C2×C411yescharacteristic, complemented
129#13093994—21no—
130#13093994—21no—
131#13093994—21no—
132#13093992—21no—
133#13093992—21no—
134Q8×Dic47C2×C411yescharacteristic, complemented
135C4×D188—21no—
136D4×Dic47—21no—
137D4×Dic47C2×C411yescharacteristic, complemented
138#13093986—21no—
139#13093986C2×C411yescharacteristic, complemented
140#13093986C2×C411yescharacteristic, complemented
141C4×C22⋊D47—28no—
142C4×C22⋊D47—21no—
143C4×C22⋊D47C2×C411yescharacteristic
144C4×C22⋊D47C2×C411yescharacteristic
145C4×C22⋊D47C2×C411yescharacteristic
146C4×C22⋊D47C2×C411yescharacteristic
147C4×C22⋊D47D411yescharacteristic
148C4×C22⋊D47D411yescharacteristic
149C4×C22⋊D47D411yescharacteristic
150C4×C22⋊D47D411yescharacteristic
151(C22⋊D47)⋊C4—21no—
152(C22⋊D47)⋊C4—21no—
153(C22⋊D47)⋊C4—21no—
154(C22⋊D47)⋊C4—21no—
155#13093982—21no—
156#13093982C2×C411yescharacteristic, complemented
157#13093981—21no—
158C2×C4⋊Dic47C2×C411yescharacteristic, complemented
159C2×Dic47⋊C4—21no—
160C2×Dic47⋊C4D411yescharacteristic
161C4⋊C4×D47C2×C411yescharacteristic, complemented
162C2×C22⋊Dic47—21no—
163C2×C22⋊Dic47D411yescharacteristic
164C2×(C2×D47)⋊C4—21no—
165C2×(C2×D47)⋊C4—21no—
166C2×(C2×D47)⋊C4—21no—
167C2×(C2×D47)⋊C4D411yescharacteristic
168C22⋊C4×D47—21no—
169C22⋊C4×D47—21no—
170C2×C4×Dic47—21no—
171C2×C4×Dic47—21no—
172C2×C4×Dic47—21no—
173C2×C4×Dic47—21no—
174C2×C4×Dic47C2311yescharacteristic
175Dic47⋊C8—21no—
176Dic47⋊C8—21no—
177C22⋊(C47⋊C8)—21no—
178C22⋊(C47⋊C8)C2311yescharacteristic
179C22⋊(C47⋊C8)C2311yescharacteristic
180(C2×D47)⋊C8—21no—
181(C2×D47)⋊C8—21no—
182#13093934—21no—
183C8×Dic47—21no—
184C47⋊#95—21no—
185C47⋊#95—21no—
186C47⋊#95C2311yescharacteristic
187C47⋊#95C2311yescharacteristic
188C2×#41×C47C2×C411yescharacteristic, complemented
189C23×C4×C47—21no—
190C23×C4×C47C2311yescharacteristic
191C2×M16×C47—21no—
192#123×C47—21no—
193C22⋊Q8×C47C2×C411yescharacteristic, complemented
194C22⋊Q8×C47C2311yescharacteristic
195#121×C47C2×C411yescharacteristic, complemented
196#121×C47C2311yescharacteristic
197#120×C47—21no—
198C4×D4×C47—21no—
199C4×D4×C47—21no—
200#117×C47C2×C411yescharacteristic, complemented
201C22⋊C8×C47—21no—
202C22⋊C8×C47C2311yescharacteristic
203C22⋊C8×C47C2311yescharacteristic
204#95×C47—21no—
205#95×C47C2311yescharacteristic
206#95×C47C2311yescharacteristic
207C24×C47C2×D411yescharacteristic
208C23×D47—21no—
209C23×D47—21no—
210C23×D47C2×D411yescharacteristic
211#41×C47—81no—
212C2×Q8×C47C22×C411yescharacteristic
213C2×D4×C47—21no—
214C2×D4×C47—21no—
215C2×D4×C47—21no—
216C2×D4×C47C22×C411yescharacteristic
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—24no—
220C22×C4×C47—21no—
221C22×C4×C47—81no—
222C22×C4×C47—81no—
223C22×C4×C47—81no—
224C22×C4×C47C22×C411yescharacteristic
225C22×C4×C47C22×C411yescharacteristic
226C22×C4×C47C2×D411yescharacteristic
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2411yescharacteristic
230C2×C22⋊D47—24no—
231C2×C22⋊D47—21no—
232C2×C22⋊D47—21no—
233C2×C22⋊D47—21no—
234C2×C22⋊D47—21no—
235C2×C22⋊D47—21no—
236C2×C22⋊D47—21no—
237C2×C22⋊D47—21no—
238C2×C22⋊D47—21no—
239C2×C22⋊D47—81no—
240C2×C22⋊D47—81no—
241C2×C22⋊D47C22⋊C411yescharacteristic
242C2×C22⋊D47C22⋊C411yescharacteristic
243C2×C22⋊D47C22⋊C411yescharacteristic
244C2×C22⋊D47C22⋊C411yescharacteristic
245C22×Dic47—21no—
246C22×Dic47—21no—
247C22×Dic47—21no—
248C22×Dic47—21no—
249C22×Dic47C2×D411yescharacteristic
250C22×Dic47C2×D411yescharacteristic
251C22×Dic47C2×D411yescharacteristic
252#10625354—81no—
253#10625352—81no—
254#10625352—81no—
255D4×D47—44no—
256D4×D47—81no—
257D4×D47—81no—
258D4×D47—81no—
259C2×D188—21no—
260C2×D188—21no—
261C2×D188—21no—
262C2×D188—21no—
263C2×D188—81no—
264C2×D188C22×C411yescharacteristic
265C2×D188C22×C411yescharacteristic
266C2×C4×D47—21no—
267C2×C4×D47—24no—
268C2×C4×D47—21no—
269C2×C4×D47—21no—
270C2×C4×D47—21no—
271C2×C4×D47—81no—
272C2×C4×D47—81no—
273C2×C4×D47—81no—
274C2×C4×D47C22×C411yescharacteristic
275C2×C4×D47C22×C411yescharacteristic
276C2×C4×D47C2×D411yescharacteristic
277C2×C4×D47C2×D411yescharacteristic
278C2×Dic94—21no—
279M16×C47—81no—
280C2×C8×C47—21no—
281C2×C8×C47—21no—
282C4⋊C4×C47—21no—
283C4⋊C4×C47—21no—
284C4⋊C4×C47C22×C411yescharacteristic
285C4⋊C4×C47C22×C411yescharacteristic
286C22⋊C4×C47—21no—
287C22⋊C4×C47—21no—
288C22⋊C4×C47—21no—
289C22⋊C4×C47—21no—
290C22⋊C4×C47—21no—
291C42×C47—21no—
292C22⋊Dic47—24no—
293C22⋊Dic47—21no—
294C22⋊Dic47—21no—
295C22⋊Dic47C22⋊C411yescharacteristic
296C22⋊Dic47C22⋊C411yescharacteristic
297C22⋊Dic47C22⋊C411yescharacteristic
298C22⋊Dic47C22⋊C411yescharacteristic
299(C2×D47)⋊C4—24no—
300(C2×D47)⋊C4—21no—
301(C2×D47)⋊C4—21no—
302(C2×D47)⋊C4—21no—
303(C2×D47)⋊C4—21no—
304(C2×D47)⋊C4—21no—
305(C2×D47)⋊C4—21no—
306(C2×D47)⋊C4—21no—
307(C2×D47)⋊C4—21no—
308(C2×D47)⋊C4—21no—
309(C2×D47)⋊C4—21no—
310(C2×D47)⋊C4—21no—
311(C2×D47)⋊C4—21no—
312(C2×D47)⋊C4C22⋊C411yescharacteristic
313(C2×D47)⋊C4C22⋊C411yescharacteristic
314(C2×D47)⋊C4C22⋊C411yescharacteristic
315(C2×D47)⋊C4C22⋊C411yescharacteristic
316C4⋊Dic47—21no—
317C4⋊Dic47—21no—
318C4⋊Dic47—21no—
319C4⋊Dic47C22×C411yescharacteristic
320C4⋊Dic47C22×C411yescharacteristic
321Dic47⋊C4—24no—
322Dic47⋊C4—21no—
323Dic47⋊C4—21no—
324Dic47⋊C4—21no—
325Dic47⋊C4—21no—
326Dic47⋊C4C22⋊C411yescharacteristic
327Dic47⋊C4C22⋊C411yescharacteristic
328Dic47⋊C4C22⋊C411yescharacteristic
329Dic47⋊C4C22⋊C411yescharacteristic
330C4×Dic47—24no—
331C4×Dic47—21no—
332C4×Dic47—21no—
333C4×Dic47—81no—
334C4×Dic47—81no—
335C4×Dic47—81no—
336C4×Dic47C22×C411yescharacteristic
337C4×Dic47C22×C411yescharacteristic
338C4×Dic47C2×D411yescharacteristic
339C4×Dic47C2×D411yescharacteristic
340C2×C47⋊C8—21no—
341C2×C47⋊C8—21no—
342C2×C47⋊C8—81no—
343#10625324—81no—
344C8×D47—81no—
345C23×C47—21no—
346C23×C47—21no—
347C23×C47—22no—
348C23×C47—21no—
349C23×C47—41no—
350C23×C47C2×C22⋊C411yescharacteristic
351C23×C47C2×C22⋊C411yescharacteristic
352C23×C47C22×D411yescharacteristic
353C22×D47—21no—
354C22×D47—21no—
355C22×D47—22no—
356C22×D47—21no—
357C22×D47—21no—
358C22×D47—41no—
359C22×D47—42no—
360C22×D47—42no—
361C22×D47—81no—
362C22×D47—81no—
363C22×D47—81no—
364C22×D47—81no—
365C22×D47C2×C22⋊C411yescharacteristic
366C22×D47C2×C22⋊C411yescharacteristic
367Q8×C47—41no—
368D4×C47—41no—
369D4×C47—41no—
370D4×C47—41no—
371D4×C47—42no—
372D4×C47—81no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—21no—
376C2×C4×C47—21no—
377C2×C4×C47—21no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—81no—
389C2×C4×C47—84no—
390C2×C4×C47C2×C22⋊C411yescharacteristic
391C2×C4×C47C2×C22⋊C411yescharacteristic
392C2×C4×C47C23×C411yescharacteristic
393C2×C4×C47C22×D411yescharacteristic
394C22⋊D47—22no—
395C22⋊D47—22no—
396C22⋊D47—22no—
397C22⋊D47—41no—
398C22⋊D47—41no—
399C22⋊D47—41no—
400C22⋊D47—41no—
401C22⋊D47—42no—
402C22⋊D47—81no—
403C22⋊D47—81no—
404C22⋊D47—81no—
405C22⋊D47—81no—
406C22⋊D47—81no—
407C22⋊D47#10414yes—
408C2×Dic47—21no—
409C2×Dic47—21no—
410C2×Dic47—22no—
411C2×Dic47—22no—
412C2×Dic47—22no—
413C2×Dic47—21no—
414C2×Dic47—21no—
415C2×Dic47—41no—
416C2×Dic47—41no—
417C2×Dic47—41no—
418C2×Dic47—41no—
419C2×Dic47—41no—
420C2×Dic47—81no—
421C2×Dic47—81no—
422C2×Dic47C2×C22⋊C411yescharacteristic
423C2×Dic47C2×C22⋊C411yescharacteristic
424C2×Dic47C2×C22⋊C411yescharacteristic
425C2×Dic47C2×C22⋊C411yescharacteristic
426C2×Dic47C2×C22⋊C411yescharacteristic
427C2×Dic47C2×C22⋊C411yescharacteristic
428D188—41no—
429D188—41no—
430D188—42no—
431D188—81no—
432D188—81no—
433D188—81no—
434C4×D47—41no—
435C4×D47—41no—
436C4×D47—41no—
437C4×D47—41no—
438C4×D47—42no—
439C4×D47—81no—
440C4×D47—81no—
441C4×D47—81no—
442C4×D47—84no—
443Dic94—81no—
444C8×C47—41no—
445C8×C47—41no—
446C47⋊C8—41no—
447C47⋊C8—41no—
448#17547—471nomaximal, Sylow
449C22×C47—21no—
450C22×C47—21no—
451C22×C47—21no—
452C22×C47—21no—
453C22×C47—21no—
454C22×C47—21no—
455C22×C47—21no—
456C22×C47—42no—
457C22×C47—42no—
458C22×C47—41no—
459C22×C47—41no—
460C22×C47—41no—
461C22×C47C2×#10412yes—
462C22×C47C22×C22⋊C411yescharacteristic
463C22×C47#57611yescharacteristic
464C22×C47#57711yescharacteristic
465C2×D47—21no—
466C2×D47—21no—
467C2×D47—21no—
468C2×D47—21no—
469C2×D47—21no—
470C2×D47—42no—
471C2×D47—42no—
472C2×D47—41no—
473C2×D47—41no—
474C2×D47—41no—
475C2×D47—41no—
476C2×D47—41no—
477C2×D47—41no—
478C2×D47—162no—
479C2×D47—162no—
480C2×D47C2×#10412yes—
481C4×C47—21no—
482C4×C47—21no—
483C4×C47—21no—
484C4×C47—21no—
485C4×C47—42no—
486C4×C47—42no—
487C4×C47—41no—
488C4×C47—41no—
489C4×C47—41no—
490Dic47—21no—
491Dic47—21no—
492Dic47—21no—
493Dic47—21no—
494Dic47—21no—
495Dic47—42no—
496Dic47—42no—
497Dic47—41no—
498Dic47—41no—
499Dic47C2×#10412yes—
500#3519—471no—
501#2974—471no—
502#2275—471no—
503#1509—471no—
504#1507—471no—
505#1507—471no—
506#1505—471no—
507#1504—471no—
508#1504D4711yescharacteristic, complemented
509#1502—471no—
510#1501—471no—
511#1501—471no—
512#1500—471no—
513C2×#327—471no—
514C2×#327—471no—
515C2×C47—21no—
516C2×C47—21no—
517C2×C47—22no—
518C2×C47—41no—
519C2×C47—81no—
520C2×C47#288311yescharacteristic
521C2×C47#289711yescharacteristic
522C2×C47C22×#10411yescharacteristic
523D47—22no—
524D47—41no—
525D47—81no—
526D47—81no—
527#555—471no—
528#554—471no—
529#553—471no—
530#553—471no—
531#553—941no—
532#550—471no—
533#546—471no—
534#546—471no—
535#546—941no—
536#546—941no—
537D42—471no—
538D42—941no—
539#540—941no—
540#538—941no—
541#538—941no—
542#532—471no—
543#529—471no—
544#525—471no—
545#525C2×D4711yescharacteristic
546C2×#121—471no—
547C2×#121—471no—
548#518—941no—
549C2×C4×D4—471no—
550C2×C4×D4—941no—
551#436—941no—
552#435—941no—
553#435—941no—
554C8×D4—941no—
555#432—471no—
556#431—471no—
557#407—471no—
558#407C2×D4711yescharacteristic, complemented
559C2×C22⋊C8—471no—
560C2×C22⋊C8—471no—
561C4×C4⋊C4—471no—
562C4×C4⋊C4—941no—
563C4×C22⋊C4—471no—
564C4×C22⋊C4—471no—
565C4×C22⋊C4—941no—
566C4×C22⋊C4—941no—
567#376—471no—
568C2×#95—471no—
569C2×#95C2×D4711yescharacteristic, complemented
570#328—471no—
571#328—471no—
572#328C2×D4711yescharacteristic, complemented
573#328C2×D4711yescharacteristic, complemented
574#327—471no—
575#327—471no—
576#327—471no—
577#327—471no—
578#327—471no—
579#327—471no—
580#327—471no—
581#327—471no—
582#327—471no—
583#327—471no—
584#327C2×D4711yescharacteristic, complemented
585#327C2×D4711yescharacteristic, complemented
586C47#1754711yescharacteristic, complemented, Sylow
587C2×#41—471no—
588C2×#41—941no—
589C2×#41C4×D4711yescharacteristic, complemented
590C22×D4—471no—
591C22×D4—471no—
592C22×D4—471no—
593C22×D4—941no—
594C22×D4—941no—
595C22×D4—941no—
596C23×C4—21no—
597C23×C4—471no—
598C23×C4—941no—
599C23×C4C22×D4711yescharacteristic
600C2×M16—21no—
601C2×M16—941no—
602C22×C8—941no—
603C22×C8—941no—
604C4⋊Q8—471no—
605#127—471no—
606#127—941no—
607#126—941no—
608#126—941no—
609#126—941no—
610#125—471no—
611#125—941no—
612#124—471no—
613#124—941no—
614#124—941no—
615#124—941no—
616#123—21no—
617#123—941no—
618#123—941no—
619#123—941no—
620#123—941no—
621#123—941no—
622#123—941no—
623C22⋊Q8—471no—
624C22⋊Q8—941no—
625C22⋊Q8—941no—
626C22⋊Q8C4×D4711yescharacteristic, complemented
627C22⋊Q8C22×D4711yescharacteristic
628#121—471no—
629#121—471no—
630#121—471no—
631#121—471no—
632#121—471no—
633#121—471no—
634#121—471no—
635#121—941no—
636#121—941no—
637#121—941no—
638#121—941no—
639#121—941no—
640#121—941no—
641#121—941no—
642#121—941no—
643#121—941no—
644#121—941no—
645#121—941no—
646#121—941no—
647#121—941no—
648#121C4×D4711yescharacteristic, complemented
649#121C22×D4711yescharacteristic
650#120—21no—
651#120—941no—
652#120—941no—
653#120—941no—
654#120—941no—
655#120—941no—
656C4×Q8—471no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—471no—
660C4×D4—471no—
661C4×D4—471no—
662C4×D4—471no—
663C4×D4—471no—
664C4×D4—471no—
665C4×D4—471no—
666C4×D4—471no—
667C4×D4—471no—
668C4×D4—471no—
669C4×D4—471no—
670C4×D4—941no—
671C4×D4—941no—
672C4×D4—941no—
673C4×D4—941no—
674C4×D4—941no—
675C4×D4—941no—
676C4×D4—941no—
677C4×D4—941no—
678C4×D4—948no—
679#117—471no—
680#117—941no—
681#117—941no—
682#117C4×D4711yescharacteristic, complemented
683C2×C4⋊C4—471no—
684C2×C4⋊C4—471no—
685C2×C4⋊C4—471no—
686C2×C4⋊C4—941no—
687C2×C22⋊C4—471no—
688C2×C22⋊C4—471no—
689C2×C22⋊C4—941no—
690C2×C22⋊C4—941no—
691C2×C22⋊C4—941no—
692C2×C22⋊C4—941no—
693C2×C22⋊C4—941no—
694C2×C22⋊C4—941no—
695C2×C42—471no—
696C2×C42—941no—
697C2×C42—941no—
698C2×C42—941no—
699C2×C42—941no—
700C4⋊C8—941no—
701C4⋊C8—941no—
702C22⋊C8—21no—
703C22⋊C8—471no—
704C22⋊C8—471no—
705C22⋊C8—941no—
706C22⋊C8—941no—
707C22⋊C8—941no—
708C22⋊C8C22×D4711yescharacteristic
709C22⋊C8C22×D4711yescharacteristic
710#97—941no—
711C4×C8—941no—
712#95—21no—
713#95—471no—
714#95—471no—
715#95—941no—
716#95—941no—
717#95C22×D4711yescharacteristic
718#95C22×D4711yescharacteristic
719C24—471no—
720C24—941no—
721C24—941no—
722C24D4×D4711yescharacteristic
723#41—81no—
724#41—3761no—
725#41—3761no—
726#41—3761no—
727C2×Q8—941no—
728C2×Q8C2×C4×D4711yescharacteristic
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—471no—
733C2×D4—471no—
734C2×D4—471no—
735C2×D4—471no—
736C2×D4—471no—
737C2×D4—471no—
738C2×D4—941no—
739C2×D4—941no—
740C2×D4—941no—
741C2×D4—941no—
742C2×D4—941no—
743C2×D4—941no—
744C2×D4—944no—
745C2×D4—941no—
746C2×D4—941no—
747C2×D4—941no—
748C2×D4—941no—
749C2×D4—941no—
750C2×D4—941no—
751C2×D4—3761no—
752C2×D4—3761no—
753C2×D4—3761no—
754C2×D4—3761no—
755C2×D4—3761no—
756C2×D4—3761no—
757C2×D4—1884no—
758C2×D4C2×C4×D4711yescharacteristic
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—24no—
762C22×C4—21no—
763C22×C4—81no—
764C22×C4—81no—
765C22×C4—81no—
766C22×C4—471no—
767C22×C4—471no—
768C22×C4—471no—
769C22×C4—471no—
770C22×C4—471no—
771C22×C4—471no—
772C22×C4—471no—
773C22×C4—941no—
774C22×C4—941no—
775C22×C4—941no—
776C22×C4—941no—
777C22×C4—944no—
778C22×C4—941no—
779C22×C4—941no—
780C22×C4—941no—
781C22×C4—941no—
782C22×C4—3761no—
783C22×C4—3761no—
784C22×C4—3761no—
785C22×C4C2×C4×D4711yescharacteristic
786C22×C4C2×C4×D4711yescharacteristic
787C22×C4D4×D4711yescharacteristic
788C22×C4D4×D4711yescharacteristic
789C22×C4D4×D4711yescharacteristic
790C22×C4C23×D4711yescharacteristic
791M16—81no—
792M16—3761no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—941no—
796C2×C8—941no—
797C2×C8—3761no—
798C2×C8—3761no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—471no—
802C4⋊C4—471no—
803C4⋊C4—471no—
804C4⋊C4—471no—
805C4⋊C4—471no—
806C4⋊C4—471no—
807C4⋊C4—941no—
808C4⋊C4—941no—
809C4⋊C4—941no—
810C4⋊C4—941no—
811C4⋊C4—941no—
812C4⋊C4—941no—
813C4⋊C4—944no—
814C4⋊C4—941no—
815C4⋊C4C2×C4×D4711yescharacteristic
816C4⋊C4C2×C4×D4711yescharacteristic
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—471no—
823C22⋊C4—471no—
824C22⋊C4—471no—
825C22⋊C4—471no—
826C22⋊C4—471no—
827C22⋊C4—471no—
828C22⋊C4—471no—
829C22⋊C4—471no—
830C22⋊C4—941no—
831C22⋊C4—941no—
832C22⋊C4—941no—
833C22⋊C4—941no—
834C22⋊C4—941no—
835C22⋊C4—941no—
836C22⋊C4—941no—
837C22⋊C4—941no—
838C22⋊C4—944no—
839C22⋊C4—941no—
840C22⋊C4—941no—
841C22⋊C4—944no—
842C22⋊C4—941no—
843C22⋊C4—941no—
844C22⋊C4—941no—
845C22⋊C4—941no—
846C42—21no—
847C42—471no—
848C42—471no—
849C42—471no—
850C42—471no—
851C42—941no—
852C42—941no—
853C42—944no—
854C42—3761no—
855C42—3761no—
856C42—3761no—
857C23—22no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—41no—
862C23—471no—
863C23—471no—
864C23—942no—
865C23—941no—
866C23—941no—
867C23—941no—
868C23—941no—
869C23—3761no—
870C23—3761no—
871C23—3761no—
872C23—3761no—
873C23—1881no—
874C23—1882no—
875C23—1882no—
876C23C22⋊C4×D4711yescharacteristic
877C23C22⋊C4×D4711yescharacteristic
878C23C2×D4×D4711yescharacteristic
879Q8—41no—
880Q8—3761no—
881D4—41no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—81no—
886D4—474no—
887D4—942no—
888D4—942no—
889D4—942no—
890D4—3761no—
891D4—3761no—
892D4—3761no—
893D4—3761no—
894D4—3761no—
895D4—3761no—
896D4—3761no—
897D4—3761no—
898D4—1881no—
899D4—1881no—
900D4—1882no—
901D4—1882no—
902D4—1881no—
903D4—1881no—
904D4—1881no—
905D4—1881no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—81no—
922C2×C4—84no—
923C2×C4—471no—
924C2×C4—471no—
925C2×C4—471no—
926C2×C4—471no—
927C2×C4—471no—
928C2×C4—471no—
929C2×C4—942no—
930C2×C4—941no—
931C2×C4—941no—
932C2×C4—942no—
933C2×C4—942no—
934C2×C4—941no—
935C2×C4—941no—
936C2×C4—3761no—
937C2×C4—3761no—
938C2×C4—3761no—
939C2×C4—3764no—
940C2×C4—3761no—
941C2×C4—3761no—
942C2×C4—1881no—
943C2×C4—1881no—
944C2×C4—1881no—
945C2×C4—1881no—
946C2×C4—1882no—
947C2×C4—1881no—
948C2×C4—1881no—
949C2×C4—1881no—
950C2×C4—1881no—
951C2×C4—1881no—
952C2×C4C22⋊C4×D4711yescharacteristic
953C2×C4C22⋊C4×D4711yescharacteristic
954C2×C4C22×C4×D4711yescharacteristic
955C2×C4C2×D4×D4711yescharacteristic
956C8—41no—
957C8—41no—
958C8—1881no—
959C8—1881no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—42no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—472no—
973C22—941no—
974C22—941no—
975C22—941no—
976C22—941no—
977C22—941no—
978C22—1882no—
979C22—1882no—
980C22—1881no—
981C22—1881no—
982C22—1881no—
983C22—1881no—
984C22—1881no—
985C22—1881no—
986C22—7522no—
987C22—7522no—
988C22#104×D4712yes—
989C22C2×C22⋊C4×D4711yescharacteristic
990C22#1568992711yescharacteristic
991C22#1568993211yescharacteristic
992C4—21no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—41no—
1001C4—472no—
1002C4—941no—
1003C4—941no—
1004C4—941no—
1005C4—941no—
1006C4—941no—
1007C4—1882no—
1008C4—1882no—
1009C4—1881no—
1010C4—1881no—
1011C2—21no—
1012C2—21no—
1013C2—22no—
1014C2—41no—
1015C2—81no—
1016C2—942no—
1017C2—3761no—
1018C2—3761no—
1019C2—1881no—
1020C2#2025184611yescharacteristic
1021C2#2025191211yescharacteristic
1022C2C2×#104×D4711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1504C2
socleC22×C47C22×C22⋊C4
prime radical#20257408C2
cosocleC22×C4×C47C24
hypercenter#1504D47
hypocenterC47#17547
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #20252424C2semidirect
3. #20245746C2semidirect
4. #20241912C2semidirect
5. #20241905C2semidirect
6. #20241902C2semidirect
7. #20241894C2semidirect
8. #20241891C2semidirect
9. #20241881C2semidirect
10. #20241879C2semidirect
11. #20241878C2semidirect
12. #20241873C2semidirect
13. C2×#15688856C2semidirect
14. #327×D47C2semidirect
15. C47×#1504C2semidirect
16. #15689836C4semidirect
17. #15689831C4semidirect
18. #15689825C4semidirect
20. #15689817C4semidirect
21. #15689792C4semidirect
23. #15689764C4semidirect
24. #15689761C4semidirect
26. #15689757C4semidirect
43. #15689177C22semidirect
44. #15689173C22semidirect
45. #15689085C22semidirect
46. C2×C22⋊(C47⋊C8)C22semidirect
47. C22⋊C8×D47C22semidirect
49. #15688974C22semidirect
51. C4×C22⋊Dic47C22semidirect
53. #15688970C22semidirect
54. #15688968C22semidirect
55. #95×D47C22semidirect
56. #15688860C22semidirect
57. #15688860C22semidirect
60. #15688858C22semidirect
61. #15688858C22semidirect
62. #15688857C22semidirect
63. #15688857C22semidirect
66. #15688856C22semidirect
67. #15688856C22semidirect
69. C47×#407C22semidirect
70. C2×#95×C47C22semidirect
71. C47×#328C22semidirect
72. C47×#328C22semidirect
73. C47×#327C22semidirect
74. C47×#327C22semidirect
75. C2×#10625354C2×C4semidirect
77. C22×D188C2×C4semidirect
82. C2×D4×D47C2×C4semidirect
88. #13094023C2×C4semidirect
90. #13094020C2×C4semidirect
94. #13094015C2×C4semidirect
96. #13094013C2×C4semidirect
108. #13094000C2×C4semidirect
110. #13093999C2×C4semidirect
111. #13093999C2×C4semidirect
115. #13093998C2×C4semidirect
116. #13093998C2×C4semidirect
128. #13093995C2×C4semidirect
134. Q8×Dic47C2×C4semidirect
137. D4×Dic47C2×C4semidirect
139. #13093986C2×C4semidirect
140. #13093986C2×C4semidirect
156. #13093982C2×C4semidirect
158. C2×C4⋊Dic47C2×C4semidirect
161. C4⋊C4×D47C2×C4semidirect
188. C2×#41×C47C2×C4semidirect
193. C22⋊Q8×C47C2×C4semidirect
195. #121×C47C2×C4semidirect
200. #117×C47C2×C4semidirect
508. #1504D47semidirect
558. #407C2×D47semidirect
569. C2×#95C2×D47semidirect
572. #328C2×D47semidirect
573. #328C2×D47semidirect
584. #327C2×D47semidirect
585. #327C2×D47semidirect
586. C47#17547semidirect
589. C2×#41C4×D47semidirect
626. C22⋊Q8C4×D47semidirect
648. #121C4×D47semidirect
682. #117C4×D47semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202574082
#202524242
#202457462
#202419122
#202419052
#202419022
#202418942
#202418912
#202418812
#202418792
#202418782
#202418732
C2×#156888562
#327×D472
C47×#15042
#1754747